e-books in this category

Symmetry and Separation of Variables
by Willard Miller - Addison-Wesley , 1977This volume is concerned with the relationship between symmetries of a linear second-order partial differential equation of mathematical physics and the coordinate systems in which the equation admits solutions via separation of variables.(3666 views)

Introduction to the Method of Multiple Scales
by Per Jakobsen - arXiv , 2014These lecture notes give an introduction to perturbation method with main focus on the method of multiple scales as it applies to pulse propagation in nonlinear optics. Aimed at students that have little or no background in perturbation methods.(3377 views)

Linear Elliptic Equations of Second Order
by Erich Miersemann - Leipzig University , 2012These lecture notes are intended as an introduction to linear second order elliptic partial differential equations. From the table of contents: Potential theory; Perron's method; Maximum principles; A discrete maximum principle.(2226 views)

Partial Differential Equations
by Erich Miersemann - Leipzig University , 2012These lecture notes are intended as a straightforward introduction to partial differential equations which can serve as a textbook for undergraduate and beginning graduate students. Some material of the lecture notes was taken from some other books.(4673 views)

Partial Differential Equations with Maple
by Robert Piche, Keijo Ruohonen - Tampere University of Technology , 1997The course presents the basic theory and solution techniques for the partial differential equation problems most commonly encountered in science. The student is assumed to know something about linear algebra and ordinary differential equations.(3387 views)

Lectures on Partial Differential Equations
by G.B. Folland - Tata Institute of Fundamental Research , 1983The purpose of this course was to introduce students to the applications of Fourier analysis -- by which I mean the study of convolution operators as well as the Fourier transform itself -- to partial differential equations.(4994 views)

Lectures on Cauchy Problem
by Sigeru Mizohata - Tata Institute of Fundamental Research , 1965A Cauchy problem in mathematics asks for the solution of a partial differential equation that satisfies certain conditions which are given on a hypersurface in the domain. Cauchy problems are an extension of initial value problems.(3827 views)

An Introduction to Microlocal Analysis
by Richard B. Melrose, Gunther Uhlmann - MIT , 2008The origin of scattering theory is the study of quantum mechanical systems. The scattering theory for perturbations of the flat Laplacian is discussed with the approach via the solution of the Cauchy problem for the corresponding perturbed equation.(4775 views)

Lectures on Elliptic Partial Differential Equations
by J.L. Lions - Tata Institute of Fundamental Research , 1957In these lectures we study the boundary value problems associated with elliptic equation by using essentially L2 estimates (or abstract analogues of such estimates). We consider only linear problem, and we do not study the Schauder estimates.(4018 views)

Nonlinear Partial Differential Equations of Elliptic Type
by Vicentiu Radulescu - arXiv , 2005This textbook provides the background which is necessary to initiate work on a Ph.D. thesis in Applied Nonlinear Analysis. The purpose is to provide a broad perspective in the subject. The level is aimed at beginning graduate students.(3998 views)

Introduction to Partial Differential Equations
by John Douglas Moore - UCSB , 2003The author develops the most basic ideas from the theory of partial differential equations, and apply them to the simplest models arising from physics. He presents some of the mathematics that can be used to describe the vibrating circular membrane.(6756 views)

Pseudodifferential Operators and Nonlinear PDE
by Michael E. Taylor - Birkhäuser Boston , 1991Since the 1980s, the theory of pseudodifferential operators has yielded many significant results in nonlinear PDE. This monograph is devoted to a summary and reconsideration of some uses of this important tool in nonlinear PDE.(4183 views)

Introduction to the Numerical Integration of PDEs
by B. Piette - University of Durham , 2004In these notes, we describe the design of a small C++ program which solves numerically the sine-Gordon equation. The program is build progressively to make it multipurpose and easy to modify to solve any system of partial differential equations.(6291 views)

An Introduction to D-Modules
by Jean-Pierre Schneiders - Universite de Liege , 1991These notes introduce the reader to the algebraic theory of systems of partial differential equations on a complex analytic manifold. We start by explaining how to switch from the classical point of view to the point of view of algebraic analysis.(3962 views)

Partial Differential Equations: An Introduction
by A.D.R. Choudary, Saima Parveen, Constantin Varsan - arXiv , 2010This book encompasses both traditional and modern methods treating partial differential equation (PDE) of first order and second order. There is a balance in making a selfcontained mathematical text and introducing new subjects.(7802 views)

Entropy and Partial Differential Equations
by Lawrence C. Evans - UC Berkeley , 2003This course surveys various uses of 'entropy' concepts in the study of PDE, both linear and nonlinear. This is a mathematics course, the main concern is PDE and how various notions involving entropy have influenced our understanding of PDE.(11199 views)

Exterior Differential Systems and Euler-Lagrange Partial Differential Equations
by R. Bryant, P. Griffiths, D. Grossman - University Of Chicago Press , 2008The authors present the results of their development of a theory of the geometry of differential equations, focusing especially on Lagrangians and Poincare-Cartan forms. They also cover certain aspects of the theory of exterior differential systems.(9355 views)

Partial Differential Equations of Mathematical Physics
by William W. Symes - Rice University , 2006This course aims to make students aware of the physical origins of the main partial differential equations of classical mathematical physics, including the equations of fluid and solid mechanics, thermodynamics, and classical electrodynamics.(14277 views)

Partial Differential Equations for Finance
by Robert V. Kohn - New York University , 2003An introduction to those aspects of partial differential equations and optimal control most relevant to finance: PDE’s naturally associated to diffusion processes, Kolmogorov equations and their applications, linear parabolic equations, etc.(13152 views)